Gravitationally frozen objects and relativistic explosion in general relativity: frozars, frozons and superbursts

In general relativity (GR) the worldline of a particle is unique and invariant, proper time and world time t are two parametrization of the same events on it only, that leads to a constraint for the proper time moments relating them by t. So, at contraction of a dust shell the proper times at finite t asymptotically freeze by no reaching a moment when the surface could cross the gravitational radius. Processes in entire volume of a star freeze at first at the center, then at higher layers, and at last the surface freezes outside the gravitational radius. Therefore in GR contraction leads to formation not black holes, but frozars (from “frozen star”) with the gravitationally frozen state of matter in entire volume, where the worldlines of particles are time-like everywhere, parallel to the t-axis and each other. Frozar formation in GR is shown for a thin dust shell, a dust ball, a star of uniform density and stars with ultrarelativistic matter. In real stars local temperatures in layers grow faster than temperature on the surface, and the last one grows on t exponentially fast. As high star’s mass, as high probability of that freezing occurs faster than warming up and the frozar will has time to be formed. But at lower masses, when the freezing does not enough fast, the warming up can stop contraction and can lead to explosion. During contraction a significant part of matter appear near the surface where in GR the physical volume sufficiently grows and energy of contraction is transformed to heat with transition of matter to the radiation dominated phase. If the star did not has time to be frozen, the part of ultrarelativistic matter and radiation leaves the star quickly, which appears as relativistic explosion, and the object will observed as relativistic supernova or hypernova. The observed lack of frozars of 2-4 solar mass and flat character of mass spectrum of more massive candidates to frozars confirm these predictions of the theory. The Big Bang and some explosions in astrophysics with large energy release probably are the cases of the relativistic explosion. In the frozar theory it appears a new GR phenomenon, the gravitational crystallization, defining structure of the most compact and massive objects in particle physics, astrophysics and cosmology. Gravitational radius of the system of few frozars sufficiently exceeds the radius of each of them and, therefore, at closing up they will not be able to merge and become frozen at distances larger of their radii, forming a new state of matter – the gravitational crystal. Frozons, particles of the Planck energy, quantum fluctuations of which are frozen in their self gravitational field, also can not merge, i.e. for frozons there will be no interaction vertexes and they form only clusters and gravitational microcrystals. In astrophysics the supermassive frozen objects in the centers of star clusters, galaxies and quasars are probable gravitational supercrystals from frozars and ordinary matter. Relic frozons and frozar crystals could be the centers of inhomogeneities and also could be appear as a dark matter. If there is the backward contraction, the Universe as whole can be frozen also in the state of a global gravitational crystal which would stop the contraction.PACS: 04.20.Dg; 04.70.-s; 97.60.-s, 98.54.-hKeywords: relativistic stars, gravitational collapse, black holes, quark stars

Finite quantum field theory with rotatory quantization and gravitational regularization

At quantization of harmonic rotator, a rotational mode of planar oscillator, energy spectrum is linear on frequency and equidistant, but zero-point energy in ground state can not arise. This is in agreement with generalization of uncertainty relations to non-Hermitean canonical pairs. Quantization of waves at collective rotations of a chain of harmonic rotators allows one to model the fields with charge-conjugation and gauge symmetries. In quantum field theory (QFT) at quantization of rotational modes as harmonic rotators the observables of fields are normal ordered and zero-point energy and zero-point charge of vacuum do not arise. In this case frequencies of quanta are angular speeds of rotation of field vectors in real or field spaces and two signs of helicity correspond to a particle and an antiparticle. Photons with circular polarization and complex fields are examples of such fields, spin and isospins (charges) of particles can be related by their frequencies as angular momenta and helicities of the rotating field vectors. At rotational quantization of strings there are no zero-point energy of modes and here a conformal anomaly is absent, so spacetime dimensionality and gauge group are not fixed. In QFT the fields should be averaged in small cells of space and time, where distribution and evolution of fields are described classically, and field functions on borders of cells should be sewed. Then loop integrals are finite and the renormalized theories are invariant under reduction of the size of cells (a renormgroup with the cell regularization). The Planck scale cell is smallest because of freezing of proper times in a strong external gravitational field of the loop diagram with redshifting of frequencies up to zero. In the Standard Model and quantum gravity the loop contributions of fields, with exception of scalars, are small and the perturbation theory is convergent.

Comoving to expansion Newtonian potential of galaxies and clusters instead of dark matter

Stretching of the Newtonian potential (NP) at early epochs is investigated and it is shown that observed effects, usually ascribed to a dark matter, can by explained by such stretching only. Increasing by time a radius of the gravitationally-bound region (GBR) and conservation of gravitational energy lead to a new scenario in which values of NP in expanding volume are maintained, while in physical volume are stretched. Really, the energy conservation in expanding volume requires for NP values to be comoving to the expanding shells. In addition, the radius of gravitationally-bound region increases by time due to decreasing of expansion velocity and different shells around galaxy cease expansion at different times. Thus, as far a shell placed from galaxy, as longer it was expanded and thickened, while potential difference on its boundaries remained unchanged. This shifts the values of NP around galaxy proportional to the distance r and, as the result, the gravitational acceleration, from NP’s 1/r^2 dependence, turned to 1/r dependence, as for centrifugal acceleration. This fact naturally explains the known empirical facts, such as flatness of rotation curves and velocity-mass relationships for galaxies and velocity dispersion in clusters.

Conservative Diffusion as a Physical Mechanism for Quantum Mechanics and Gravitation

The theory of conservative diffusion and its main applications are reviewed. A basic model for the theory is diffusion of a cold light gas in a warm heavy gas before relaxation when light gas remains cold and mean energy of its particles conserves. Unlike the Lorentz gas, where thermal energies of light and heavy atoms are equal, here the same order are their thermal speeds. Such conservative diffusion is described by two equations – the Hamilton-Jacobi and continuity equations, nonlinear under the probability density. They can be linearized by introduction of a complex probability amplitude, transforming them to the Schrödinger equation where one must add not probabilities, but probability amplitudes of alternatives. Mean free path and the corresponding momentum determine an elementary phase volume and a diffusion coefficient. The theory predicts a number of quasiquantum effects in classical systems. The formalism of quantum mechanics thus describes a classical conservative diffusion and quantum mechanics is only a special case of such diffusion in the vacuum, when the elementary phase volume is equal to the Planck constant. A conservative thermodiffusion at nonzero temperature gradient is studied also. Its properties, such as decreasing of intensity of fluctuations of particles (including redshift of frequencies), drift of particles to colder region and their thermodiffusive acceleration, not depending on the mass of particles, are similar to properties of gravitation. This allows us to identify gravitation by thermodiffusion in the physical vacuum. In the diffusive picture fluctuations of energy-momentum of classical particles due to interaction with vacuum lead to increasing of their mean energy, which appears as quantum phenomena, while corresponding local decreasing of vacuum energy density reveals as gravitation. The diffusive treatment of quantum theory thus leads to the thermodiffusive treatment of gravitation too with natural synthesis of theories of both phenomena. Observable effects following from the new theory are discussed.

New effects in cosmology: frequency and intensity stasis for radiation crossed galaxy clusters

New effects of stasis of radiation due to switching out from expansion flow at crossing largest gravitationally-bound regions (GBR), such as galaxy clusters, are considered and their observational consequences for supernovae and cosmic microwave background (CMB) data are discussed. The stasis of frequency and intensity of radiation at crossing of large number of clusters appreciably decreases observing redshifts z and magnifies apparent luminosities. Only normal redshifts z’ of photons not crossed clusters are directly related with the cosmic scale factor and thus true distances exceed those which follow from z. The effects increase for distant objects because of smaller inter-cluster distances at early epochs. For the relic radiation crossed the clusters the effects lead to the stasis of its temperature and “heating” with respect to a normally expanded flow outside the cluster. As a result, instead of former paradigm about almost sterile propagation of relic radiation from the recombination epoch, there is an opposite picture. Mixing of relic radiation flows, many times isolated from the expansion flow in GBRs along path, leads to their isotropy and loss of earlier perturbations. The observing anisotropy follows from the stasis effects at crossing of multiple layers of clusters at our nearest environment. The stasis effects allow one to do more exact conclusions from data analysis and lead to revising of distances and properties of extragalactic objects.

A model of the closed universe gravitating in 4-space

Models of the closed Universe as a thin 3-sphere in 4-space, gravitating along 3-sphere’s radius, are reformulated in a new form, in which at a local environment of an observer the non-relativistic dynamics of a ball is reproduced with a correct energy conservation condition. Corresponding evolution equations for dust matter and radiation in the 3-sphere are obtained and their observational consequences are studied. It is shown that the closed models in 4-space also lead to the “Miniverse” model with a highly oscillating curve for the “distance modulus – redshift” relation.

Gravitation as a thermodiffusion in the physical vacuum

An influence of matter on the vacuum energy density is considered and a treatment of gravitation as inhomogeneity of quantum diffusion is developed. A treatment of quantum theory as conservative diffusion [1] is briefly presented, where quantum fluctuations of energy and momentum of a classical particle occur because of interaction with physical vacuum. The increasing of particle’s mean energy at such fluctuations appears as quantum phenomena, while corresponding local decreasing of mean vacuum energy to the same value appears as gravitation. For one a particle the decreasing is extremaly small and in particle physics it can be neglected. However, when large number of particles are concentrated in a small volume, consequences of the vacuum energy decreasing become appreciable and they appear as gravitation. The diffusion treatment of quantum processes thus leads to the diffusion treatment of gravitation with natural synthesis of theories of both phenomena. New properties of inhomogeneous diffusion related by local decreasing of vacuum energy, such as slowering of fluctuations of particles with delay of intensity of processes (including redshift of frequencies), drift of particles toward slower fluctuations region and their diffusive acceleration, which is independent on mass of particles, are studied. Observable effects following from the new treatment are discussed.

Theory of conservative diffusion in classical and quantum systems

In previous paper [1] conservative diffusion of light particles in a dilute medium of heavy particles was studied by analogue with Brownian motion. In the present paper the theory is formulated in more consistent “hydrodynamic” form by using a conservativity condition only, that mean energy of a light particle is conserved. As a model is taken diffusion of very cold light gas in warm heavy gas a time interval before relaxation when light gas remains cold. Unlike Lorentz’s gas, where thermal energies of light and heavy atoms are equal, here their thermal speeds are equal and this leads to the effects of conservativity similar to quantum effects. Such conservative diffusion is described by two equations – the continuity equation and the energy conservation condition, non-linear under the probability density. At introduction of a complex probability amplitude the equations linearized and turn to the Schrödinger equation. As a result, one must add not probability of alternatives, but probability amplitudes. A free pass length and corresponding momentum define an elementary phase volume and the diffusion coefficient. The predicting new quasi-quantum effects in classical systems are discussed. It is shown that the formalism of quantum mechanics describes the classical conservative diffusion with a constant diffusion coefficient and that quantum mechanics is a particular case of such diffusion in the vacuum where the elementary phase volume of free passage is equal to the Planck constant.

Models of the Universe with strongly conserved energy of matter

It is shown that earlier in the Friedmann models requirements of nonrelativistic dynamics of a dust ball, concerning the energy conservation, have not been obeyed, which then led to inconsistency at formulation of relativistic models too. It is proposed a method for reformulation of models of relativistic cosmology when at small distances they naturally coincide by the nonrelativistic model of the dust ball. As the result, in such modified model some of former problems of the Friedmann models do not arise.

A free radial falling to a common centre of inertia of two and more identical gravitationally-frozen objects – frozars (stellar mass or supermassive) and frozons (particles of Planck energy, the fluctuations of which are frozen in the self-gravitational field) is studied. Two frozars cannot merge and freeze without touch of nearest points of their surfaces, and the distances between the system’s centre of inertia and centers of frozars always exceed the system’s gravitational radius. The gravitational radius of a system of three and more frozars always several times exceeds the gravitational radius of each of frozars. For this reason the freely falling frozars freeze by forming a frozar supercrystal, where mean distances between the surfaces of frozars several times exceed a radius each of them. Frozons also cannot merge and only form frozen complexes, mainly as pairs of particle-antiparticle, up to frozon microcrystals. Frozar and frozon crystallizations appear as two fundamental general relativistic phenomena determining the structure of most compact and most massive objects in particle physics, astrophysics and cosmology. In astrophysics supermassive collapsed objects at the centre of stellar clusters, galaxies and quasars most probably are supercrystals of frozars and ordinary matter. During cosmological expansion primordial frozon and frozar crystals were centers of inhomogeneities, and also appear as a dark matter. If there will be a contraction stage, the Universe as whole also will freeze in a state of global frozar crystal and the contraction will stop, so there the cosmological singularity will absent and entropy of the Universe will be conserved. In particle physics the vertexes of interaction with frozons do not exist and compact objects having energy exceeding the Planck energy are “atoms”, “molecules” and microcrystals of frozons.